Решебник по алгебре 8 класс Мерзляк Задание 659

\[\boxed{\mathbf{659\ (659).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ x² - 4x + 3 = 0\]

\[D = 16 - 12 = 4\]

\[x = \frac{4 \pm \sqrt{4}}{2} = \frac{4 \pm 2}{2}\]

\[x_{1} = 3,\ \ x_{2} = 1\]

\[Ответ:x = 3;x = 1.\]

\[2)\ x² + 2x - 3 = 0\]

\[D = 4 + 12 = 16\]

\[x = \frac{- 2 \pm \sqrt{16}}{2} = \frac{- 2 \pm 4}{2}\]

\[x_{1} = 1,\ \ x_{2} = - 3\]

\[Ответ:\ x = - 3;x = 1.\]

\[3)\ x² + 3x - 4 = 0\]

\[D = 9 + 16 = 25\]

\[x = \frac{- 3 \pm \sqrt{25}}{2} = \frac{- 3 \pm 5}{2}\]

\[x_{1} = 1,\ \ x_{2} = - 4\]

\[Ответ:\ x = - 4;x = 1.\]

\[4)\ x² - 4x - 21 = 0\]

\[D = 16 + 4 \cdot 21 = 16 + 84 =\]

\[= 100\]

\[x = \frac{4 \pm \sqrt{100}}{2} = \frac{4 \pm 10}{2}\]

\[x_{1} = 7,\ \ x_{2} = - 3\]

\[Ответ:x = 7;\ x = - 3.\]

\[5)\ x² + x - 56 = 0\]

\[D = 1 + 4 \cdot 56 = 225\]

\[x = \frac{- 1 \pm \sqrt{225}}{2} = \frac{- 1 \pm 15}{2}\]

\[x_{1} = - 8,\ \ x_{2} = 7\]

\[Ответ:\ x = - 8;x = 7.\ \]

\[6)\ x² - 6x - 7 = 0\]

\[D = 36 + 28 = 64\]

\[x = \frac{6 \pm \sqrt{64}}{2} = \frac{6 \pm 8}{2}\]

\[x_{1} = 7,\ \ x_{2} = - 1\]

\[Ответ:\ x = - 1;x = 7.\]

\[7)\ x² - 8x + 12 = 0\]

\[D = 64 - 4 \cdot 12 = 64 - 48 = 16\]

\[x = \frac{8 \pm \sqrt{16}}{2} = \frac{8 \pm 4}{2}\]

\[x_{1} = 6,\ \ x_{2} = 2\]

\[Ответ:x = 2;x = 6.\]

\[8)\ x² + 7x + 6 = 0\]

\[D = 49 - 24 = 25\]

\[x = \frac{- 7 \pm \sqrt{25}}{2} = \frac{- 7 \pm 5}{2}\]

\[x_{1} = - 6,\ \ x_{2} = - 1\]

\[Ответ:\ x = - 1;\ x = - 6.\]

\[9) - x^{2} + 6x + 55 = 0\]

\[D = 36 + 4 \cdot 55 = 36 + 220 =\]

\[= 256\]

\[x = \frac{- 6 \pm \sqrt{256}}{- 2} = \frac{- 6 \pm 16}{- 2}\]

\[x_{1} = 11,\ \ x_{2} = - 5\]

\[Ответ:\ x = - 5;x = 11.\]

\[10)\ 2x² - 3x - 2 = 0\]

\[D = 9 + 16 = 25\]

\[x = \frac{3 \pm \sqrt{25}}{4} = \frac{3 \pm 5}{4}\]

\[x_{1} = 2,\ \ x_{2} = - 0,5\]

\[Ответ:\ x = - 0,5;x = 2.\]

\[11)\ 2x² - x - 6 = 0\]

\[D = 1 + 12 \cdot 4 = 49\]

\[x = \frac{1 \pm \sqrt{49}}{4} = \frac{1 \pm 7}{4}\]

\[x_{1} = 2,\ \ x_{2} = - 1,5\]

\[Ответ:x = - 1,5;x = 2.\]

\[12)\ 3x² - 4x - 20 = 0\]

\[D = 16 + 240 = 256\]

\[x = \frac{4 \pm \sqrt{256}}{6} = \frac{4 \pm 16}{6}\]

\[x_{1} = - 2,\ \ x_{2} = \frac{10}{3} = 3\frac{1}{3}\]

\[Ответ:\ x = - 2;x = 3\frac{1}{3}.\]

\[13)\ 10x² - 7x - 3 = 0\]

\[D = 49 + 120 = 169\]

\[x = \frac{7 \pm \sqrt{169}}{20} = \frac{7 \pm 13}{20}\]

\[x_{1} = 1,\ \ x_{2} = - 0,3\]

\[Ответ:\ x = - 0,3;x = 1.\]

\[14) - 5x^{2} + 7x - 2 = 0\]

\[D = 49 - 40 = 9\]

\[x = \frac{- 7 \pm \sqrt{9}}{- 10} = \frac{- 7 \pm 3}{- 10}\]

\[x_{1} = 1,\ \ x_{2} = 0,4\]

\[Ответ:x = 1;x = 0,4.\]

\[15) - 6x^{2} - 7x - 1 = 0\]

\[D = 49 - 24 = 25\]

\[x = \frac{7 \pm \sqrt{25}}{- 12} = \frac{7 \pm 5}{- 12}\]

\[x_{1} = - 1,\ \ x_{2} = - \frac{1}{6}\]

\[Ответ:\ x = - 1;\ x = - \frac{1}{6}.\]

\[16)\ 3x² - 10x + 3 = 0\]

\[D = 100 - 36 = 64\]

\[x = \frac{10 \pm \sqrt{64}}{6} = \frac{10 \pm 8}{6}\]

\[x_{1} = 3,\ \ x_{2} = \frac{1}{3}\]

\[Ответ:x = \frac{1}{3};x = 3.\]

\[17) - 3x^{2} + 7x + 6 = 0\]

\[D = 49 + 72 = 121\]

\[x = \frac{- 7 \pm \sqrt{121}}{- 6} = \frac{- 7 \pm 11}{- 6}\]

\[x_{1} = 3,\ \ x_{2} = - \frac{2}{3}\]

\[Ответ:\ x = - \frac{2}{3};x = 3.\]

\[18)\ x² - 4x + 1 = 0\]

\[D = 16 - 4 = 12\]

\[x = \frac{4 \pm \sqrt{12}}{2} = \frac{4 \pm 2\sqrt{3}}{2} =\]

\[= 2 \pm \sqrt{3}\]

\[Ответ:\ x = 2 \pm \sqrt{3}.\]

\[19)\ 2x² - x - 4 = 0\]

\[D = 1 + 32 = 33\]

\[x = \frac{1 \pm \sqrt{33}}{4}\]

\[Ответ:x = \frac{1 \pm \sqrt{33}}{4}.\]

\[20)\ x² - 8x + 20 = 0\]

\[D = 64 - 80 = - 16 < 0,\ \]

\[корней\ нет.\]

\[Ответ:нет\ корней.\ \]